Consider the operation is [tex]R_2\to -3R_2[/tex].
Given:
The augmented matrix below represents a system of equations.
[tex]\left[\left.\begin{matrix}1&0&1\\1&3&-1\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-9\\-2\end{matrix}\right][/tex]
To find:
Matrix results from the operation [tex]R_2\to -3R_2[/tex].
Step-by-step explanation:
We have,
[tex]\left[\left.\begin{matrix}1&0&1\\1&3&-1\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-9\\-2\end{matrix}\right][/tex]
After applying [tex]R_2\to -3R_2[/tex], we get
[tex]\left[\left.\begin{matrix}1&0&1\\-3(1)&-3(3)&-3(-1)\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-3(-9)\\-2\end{matrix}\right][/tex]
[tex]\left[\left.\begin{matrix}1&0&1\\-3&-9&3\\3&2&0\end{matrix}\right|\begin{matrix}-1\\27\\-2\end{matrix}\right][/tex]
Therefore, the correct option is A.
